See this page:

http://www.fortunecity.com/lavender/.../881/dying.htm

Thanks for the direct link

I suspect you don't have enough light for the kind of plants you are buying.
You don't say how much light you have over the tank, but if you have only an
ordinary tank hood, you probably don't have enough light to grow most aquarium
plants.

Yeah, it's the hood and neon that came with the Aquarium, I think it's
20W, but I don't have the specs anymore

PH: 8.5
KH: 60 ppm (about 3.4, I beleive is the correct conversion)

Yikes. Your pH is pretty high for that KH. Are you adding something to the
tank?

Only what I said, a water conditionner
http://www.hagen.com/canada/english/...07655001010 1
and the nitrifier
http://www.hagen.com/canada/english/...07612001010 1

NH3/NH4 (ammonia): around 0.6 ppm (test kit doesn't give super
precise result, so it's around 0.6ppm or maybe a little less)
NO2 (Nitrite): 0.1 or less ppm

Ammonia and nitrite should not be detectible in a healthy tank. Something's
wrong. How long has this tank been set up?

As I said, the test kits are not super precise and the 0.6ppm value
for amonia could be less and the 0.1ppm nitrite level is actually the
first value on the chart, so it could be less or 0 as well.
Here's the test kit that I'm using to make the tests:
http://www.hagen.com/canada/english/...001700010 101
I just noticed that this is a "pond" test kit...does that matter?

The tank has been set up aout 15 months ago.

So what would be my first immediate step then? Change the neon for a
brighter one as soon as possible?